54=(4x+1)(3x)

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Solution for 54=(4x+1)(3x) equation: 


Simplifying
54 = (4x + 1)(3x)

Reorder the terms:
54 = (1 + 4x)(3x)

Remove parenthesis around (3x)
54 = (1 + 4x) * 3x

Reorder the terms for easier multiplication:
54 = 3x(1 + 4x)
54 = (1 * 3x + 4x * 3x)
54 = (3x + 12x2)

Solving
54 = 3x + 12x2

Solving for variable 'x'.

Reorder the terms:
54 + -3x + -12x2 = 3x + -3x + 12x2 + -12x2

Combine like terms: 3x + -3x = 0
54 + -3x + -12x2 = 0 + 12x2 + -12x2
54 + -3x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
54 + -3x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -1x + -4x2) = 0

Factor a trinomial.
3((2 + -1x)(9 + 4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {2, -2.25}

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